Existence theory and numerical analysis of three species prey-predator model under Mittag-Leffler power law

Mohammed S Abdo; Satish K Panchal; Kamal Shah; Thabet Abdeljawad

doi:10.1186/s13662-020-02709-7

Existence theory and numerical analysis of three species prey-predator model under Mittag-Leffler power law

Adv Differ Equ. 2020;2020(1):249. doi: 10.1186/s13662-020-02709-7. Epub 2020 May 27.

Authors

Mohammed S Abdo^{1

2}, Satish K Panchal¹, Kamal Shah³, Thabet Abdeljawad^{4

5

6}

Affiliations

¹ Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen.
² Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India.
³ Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan.
⁴ Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.
⁵ Department of Medical Research, China Medical University, Taichung, Taiwan.
⁶ Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan.

Abstract

In this manuscript, the fractional Atangana-Baleanu-Caputo model of prey and predator is studied theoretically and numerically. The existence and Ulam-Hyers stability results are obtained by applying fixed point theory and nonlinear analysis. The approximation solutions for the considered model are discussed via the fractional Adams Bashforth method. Moreover, the behavior of the solution to the given model is explained by graphical representations through the numerical simulations. The obtained results play an important role in developing the theory of fractional analytical dynamic of many biological systems.

Keywords: Adams Bashforth method; Atangana–Baleanu and Caputo derivative; Existence and stability theory; Fixed point theorem.